# Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions

## TL;DR

This paper introduces perturbed underdamped Langevin dynamics for sampling, which maintains the original invariant measure while reducing asymptotic variance, leading to more efficient sampling methods.

## Contribution

The paper proposes a novel class of Langevin samplers with perturbations that preserve the invariant measure and improve sampling efficiency, supported by theoretical and numerical analysis.

## Key findings

- Perturbed Langevin samplers maintain the target distribution.
- Perturbations can reduce asymptotic variance.
- Numerical experiments confirm improved performance.

## Abstract

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.